Extremism watchers and civil rights groups have welcomed an appeal from Donald Trump for a halt to a surge in harassment and hate crimes, but are urging the president-elect to do more.

In an interview with CBS television network's 60 Minutes program that aired Sunday, Trump was asked about reports of threats and racial slurs hurled at minorities by some of his supporters since the Nov. 8 U.S. presidential election.

"I am so saddened to hear that," Trump said. "And I say, 'Stop it.' If it — if it helps, I will say this, and I will say right to the cameras: 'Stop it.'"

Brian Levin, director of the Center for the Study of Hate and Extremism at California State University, San Bernardino, said Trump's comment was welcome but did not go far enough in forswearing his most virulent campaign rhetoric.

FILE - A demonstrator holds a sign during a rally outside Trump Tower in New York on Saturday, Nov. 12, 2016, to protest against President-elect Donald Trump.

"His statement is welcome and appropriate but the big question is, 'What will be the discourse going forward from candidate Trump, who invoked many harmful stereotypes, versus President-elect Trump, who is in much different position right now,'" Levin said.

As a candidate, Trump labeled Mexican immigrants "rapists" and "killers," and called for a temporary ban on all Muslims entering the country.

The Southern Poverty Law Center (SPLC) called on Trump to disavow his campaign rhetoric and the "support he's received from the racists and the radical right."

Rise in hate?

Trump's comments on 60 Minutes followed reports of an unprecedented rise in hate crimes in the wake of his Nov. 8 victory.

Mark Potok, a leading expert in extremism and senior fellow with the SPLC, said his group had received some 315 reports of racially-charged incidents in the past week, more than were recorded in the wake of the September 2001 terrorist attacks, with the majority aimed at Muslims.

FILE - Women march against U.S. President-elect Donald Trump in Manhattan, New York, Nov. 13, 2016.

"We've seen a dramatic upsurge in both hate crimes and then lesser hate incidents, things like Muslim kids being bullied, Muslim women having their hijabs torn off their faces, similar kinds of incidents," Potok said.

In one incident in Columbus, Ohio, a hijab-wearing Muslim woman driving with her children and elderly parents was threatened and verbally abused by a man at a traffic stop, according to the Council on American Islamic Relations (CAIR), a Washington-based advocacy organization.

In another incident in Michigan, a man threatened to set a Muslim woman on fire with a lighter unless she took off her hijab, CAIR said.

"I think that It is pretty clear that it's Muslims who have borne the brunt of it, although remarkably the animus and hatred seems to be directed at all minorities of virtually any kind," Potok said.

After Muslims, the "primary and secondary targets" of the recent wave of hate crimes were blacks, Latinos and LGBT people, Potok said.

Just how large a spike in hate crime there has been remains uncertain, however. Several reports have been proven false, and Potok cautioned that most incidents reported to the Southern Poverty Law Center did not amount to hate crime.

Levin of California State University added that there was no "independent evidence to sustain the contention that there were more [hate crimes] in the days after the Trump election than after 9/11."

FILE - Demonstrators holds banners as they protest during a march in downtown Washington in opposition of President-elect, Donald Trump, Nov. 12, 2016.

In response to concerns about rising hate crime, the Southern Poverty Law Center last week launched an online petition calling on Trump to honor his victory speech pledge to be "president for all Americans."

Calls for tougher stand

Muslim advocates, meanwhile, called for a more forceful repudiation of the hate crimes by the president-elect.

In a study on anti-Muslim hate crime released in September, Levin found that anti-Islam incidents soared by 87.5 percent in the five days after Trump announced his controversial Muslim ban last December.

By contrast, his research found that former President George W. Bush's call for tolerance after the September 2001 terrorist attacks led to a sharp decline in hate crimes against Muslims.

"Words matter," Levin said. "The overwhelming majority of Trump's supporters are not hardened bigots at all, but they're fearful and they'll follow his cue. "

Trump's call for a stop to the harassment falls well short of Bush's speech, said Robert Thompson, a professor of television and pop culture at Syracuse University.

"I think Donald Trump could be effective now that he's been elected in making some really substantial speeches telling people to stop it, but what we saw on 60 Minutes was not a substantial speech," Thompson said.